DLVO interaction between the spheres DL-interaction energy for two spheres: D w ( x) 64c π ktrϕ e λ DL 2 x λ 2 0 0 D DLVO interaction w ( x) 64πkTRϕ e λ DLVO AR /12x 2 x λd 2 0 D
Lecture 11 Contact angle and wetting phenomena
Young s equation Drop on the surface complete spreading Establishing finite contact angle γ cosθ = γ γ L S SL γ γ S S γ > 0 partial wetting SL γ < 0 no wetting SL
Young s equation Derivation from the equilibrium condition ( γ γ ) γ 0 dg = da + da = at dv = 0 SL S SL L L π VL = a h+ h 6 2 3 ( 3 ) L 2 2 ( ) A = π a + h dasl = 2π ada AL AL dal = da + dh = 2πada + 2πhdh a h VL VL π 2 2 dvl = da + dh = π ahda + ( a + h ) dh = a h 2 0 da = 2π a cosθ da L
Line tension For small drops (<10µm) an additional energy of the wetting line should be taken into account κ γ Lcosθ = γs γsl a Estimate: at a rim a molecule has 2 bonds less (assuming simple cubic) for cyclohexane: vapu κ = = 310 3Na A mol 11 J m
If γ S > γsl + γl Complete wetting Gibbs free energy is decreased by forming a continuous film on the surface Spreading coefficient: S = γ S γsl γl Contact angle decreases with temperature due to drop in γ L. At wetting temperature Tw, S=0 and complete wetting is reached.
Capillary rise If capillary is dipped in a liquid, the liquid meniscus will either rise or lower due to surface tension h = 2γ L cosθ rgρ c Indeed: ( ) 2 dg = 2πr dh γ γ + 2πr ρghdh C S SL C
Particles at liquid-gas interface For small particles (i.e. neglecting the gravity) the equilibrium position at the interface is determined by the surface tension typically >100µm Recall stabilization of emulsion by solid particles:
Network of fibers Network of fibers with final wetting angle will prevent water from passing through; some pressure has to be applied to let it through
Measurement of the contact angle The most common technique is observation of sessile drop with a microscope θ h tan = 2 a or by using a Wilhelmy plate Wetting properties of powders can be detrmined from capillary rise Note, the contact angle depends strongly on the surface contamination
Hysteresis in contact angle measurements If we increase or decrease e.g. droplet volume a hysteresis in the angle will be observed Usually: θ adv > θ rec Causes for the contact angle hysteresis: surface roughness heterogeneity of the surface (resulting in pinning of a droplet) absorbing dissolved substances mechanical deformation of the surface due to surface tension adsorption/desorption of liquid molecules at the interface (work required!)
Surface roughness and heterogeneity Roughness increases the actual surface area and therefore decreases the apparent wetting angle for hydrophilic surface and increases it for a hydrophobic surface (Wenzel law) cosθ app = R cosθ rough Heterogeneous surfaces: Cassie equation cosθapp = f1 cosθ1+ f2 cosθ2
Theory aspects Surface tension at solid-air and solid-liquid interfaces strongly depend on the surface preparation (e.g. deformation) Experimentally only advancing and receding angles can be determined Macroscopic (Young s) contact angle is different from a microscopic one (caused by van der Waals and DL-forces, at distances <100nm)
Theory aspects Surface tension at solid-liquid is the most difficult to be accessed by the experiment Though it can be estimated based on the properties of clean interfaces (Girifalco, Good and Fowkes model) w γ w = γ1+ γ2 γ12 A A A 12 11 22 = 2 2 12πD0 12πD0 A = and γ = 11 11 11 2 11 2 24πD0 24πD0 A γ = γ + γ 2 γ γ 12 1 2 1 2
Dynamics of wetting Typical measurement geometries Apparent contact angle depends also on the speed and viscosity, that can be combined into a Capillary number: vη Ca = γ L
Dynamic of wetting and dewetting Apparent contact angle vs. speed Apparent advancing angle vs. capillary number for two mixtures of glycerol/water Despite 7 times difference in viscosity, capillary number is a good parameter for both liquids
Dynamics of wetting Liquid spreading on a solid surface movement of the drop. Heat is dissipated by eddies Thin <0.1µm precursor film binding of molecules at the front of the precursor film AFM image of PDMS drops on Si surface
Dynamics of wetting Example formation of polystyrol nanotubes in filter pores Ready nanotubes after filter dissolution
Polymer deposition and Dewetting polymers are typically deposited either by dip or spin coating if wetting angle θ>0, the film is metastable and the holes will be formed spontaneously above the glass transition temperature
Ore flotation Applications of wetting Detergency
Problems End of chapter problems: 7.1 7.2